Problem#1
Laser Surgery. Using a mixture of CO2, N2, and sometimes He, CO2 lasers emit a wavelength of 10.6 µm. At power outputs of 0.100 kW, such lasers are used for surgery. How many photons per second does a CO2 laser deliver to the tissue during its use in an operation?
Answer:
We know the power of the laser beam, so we know the energy per second that it delivers. The
wavelength of the light tells us the energy of each photon, so we can use that to calculate the number of photons delivered per second.
The energy of each photon is E = hf = hc/λ = (1.99 x 10-25 J.m)/λ.
The power is the total energy per second and the total energy Etot is the number of photons N times the energy E of each photon.
λ = 10.6 x 10-6 m, so E = (1.99 x 10-25 J.m)/(10.6 x 10-6 m) = 1.88 x 10-20 J.
P = Etot/t = NE/t, so
N/t = P/E = (0.100 x 103 W)/(1.88 x 10-20 J) = 5.32 x 1021 photons/s
Problem#2
Removing Birthmarks. Pulsed dye lasers emit light of wavelength 585 nm in 0.45-ms pulses to remove skin blemishes such as birthmarks. The beam is usually focused onto a circular spot 5.0 mm in diameter. Suppose that the output of one such laser is 20.0 W. (a) What is the energy of each photon, in eV? (b) How many photons per square millimeter are delivered to the blemish during each pulse?
Answer:
We can calculate the energy of a photon from its wavelength. Knowing the intensity of the beam and the energy of a single photon, we can determine how many photons strike the blemish with each
pulse.
The energy of each photon is E = hf = hc/λ = (1.99 x 10-25 J.m)/λ.
The power is the total energy per second and the total energy Etot is the number of photons N times the energy E of each photon. The photon beam is spread over an area A = πr2 with r = 2.5 mm.
(a) λ = 585nm = 585 x 10-9 m, so E = = (1.99 x 10-25 J.m)/(585 x 10-9 m) = 3.40 x 10-19 J = 2.12 eV
(b) P = Etot/t = NE/t, so
N = Pt/E = (20.0 W)(0.45 x 10-3 s)/(3.40 x 10-19 J) = 2.65 x 1016 photons
These photons are spread over an are πr2, so the number of photon per mm2 is
(2.65 x 1016 photons)/[π x (2.5 mm)2] = 1.35 x 1015 photons/mm2
Problem#3
How many photons per second are emitted by a 7.50 mV CO2 laser that has a wavelength of 10.6 µC.
Answer:
The number of photons emitted each second is the total energy emitted divided by
the energy of one photon. The energy of one photon is given by E = hf. E = Pt gives the energy
emitted by the laser in time t.
In 1.00 s the energy emitted by the laser is (7.50 x 10-3 W)(1.00 s) = 7.50 x 10-3 J.
The energy of each photon is
E = hc/λ = (6.626 x 10-34 J.s)(2.998 x 108 m/s)/(10.6 x 10-6 m) = 1.874 x 10-20 J.
Therefore (7.50 x 10-3 J/s)/(1.874 x 10-20 J) = 4.00 x 1017 photons/s
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